examples/SchroedingerDemo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Recompiling stale cache file /home/hofi/.julia/lib/v0.4/TSSM.ji for module TSSM.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "including tssm_fourier.jl for type Float64\n",
      "    Fourier1D\n",
      "    Fourier2D\n",
      "    Fourier3D\n",
      "    FourierReal1D\n",
      "    FourierReal2D\n",
      "    FourierReal3D\n",
      "including tssm_fourier_bessel.jl for type Float64\n",
      "    FourierBessel2D\n",
      "    FourierBesselReal2D\n",
      "    BesselRotSym1D\n",
      "    BesselRotSymReal1D\n",
      "including tssm_schroedinger.jl for type Float64\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "including tssm_schroedinger_hermite.jl for type Float64\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n",
      "including tssm_common.jl for type Float64\n",
      "    Fourier1D\n",
      "    Fourier2D\n",
      "    Fourier3D\n",
      "    FourierReal1D\n",
      "    FourierReal2D\n",
      "    FourierReal3D\n",
      "    FourierBessel2D\n",
      "    FourierBesselReal2D\n",
      "    BesselRotSym1D\n",
      "    BesselRotSymReal1D\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n",
      "including tssm_schroedinger.jl for type Float64\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n",
      "including tssm_fourier.jl for type Float128\n",
      "    Fourier1D\n",
      "    Fourier2D\n",
      "    Fourier3D\n",
      "    FourierReal1D\n",
      "    FourierReal2D\n",
      "    FourierReal3D\n",
      "including tssm_fourier_bessel.jl for type Float128\n",
      "    FourierBessel2D\n",
      "    FourierBesselReal2D\n",
      "    BesselRotSym1D\n",
      "    BesselRotSymReal1D\n",
      "including tssm_schroedinger.jl for type Float128\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "including tssm_schroedinger_hermite.jl for type Float128\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n",
      "including tssm_common.jl for type Float128\n",
      "    Fourier1D\n",
      "    Fourier2D\n",
      "    Fourier3D\n",
      "    FourierReal1D\n",
      "    FourierReal2D\n",
      "    FourierReal3D\n",
      "    FourierBessel2D\n",
      "    FourierBesselReal2D\n",
      "    BesselRotSym1D\n",
      "    BesselRotSymReal1D\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n",
      "including tssm_schroedinger.jl for type Float128\n",
      "    Schroedinger1D\n",
      "    Schroedinger2D\n",
      "    Schroedinger3D\n",
      "    SchroedingerReal1D\n",
      "    SchroedingerReal2D\n",
      "    SchroedingerReal3D\n",
      "    SchroedingerHermite1D\n",
      "    SchroedingerHermite2D\n",
      "    SchroedingerHermite3D\n",
      "    SchroedingerHermiteReal1D\n",
      "    SchroedingerHermiteReal2D\n",
      "    SchroedingerHermiteReal3D\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hofi/.julia/v0.4/Conda/deps/usr/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    }
   ],
   "source": [
    "using TSSM\n",
    "using PyPlot\n",
    "include(\"time_stepper.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f2594908890>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2594784b90>"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const omega_x = 1.1\n",
    "const hbar = 1.1\n",
    "const mass = 1.1\n",
    "const x0 = sqrt(hbar/mass/omega_x)\n",
    "const alpha = 1.1\n",
    "\n",
    "function harmonic(x)\n",
    "    0.5*mass*omega_x^2*x.^2\n",
    "end\n",
    "\n",
    "nx = 2048\n",
    "xmin = -16\n",
    "xmax = +16\n",
    "\n",
    "method = Schroedinger1D(nx, xmin, xmax, hbar=hbar, mass=mass, potential=harmonic)\n",
    "\n",
    "plot(get_nodes(method), get_potential(method))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "coherent_state (generic function with 1 method)"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function coherent_state(x, t)\n",
    "    xi = x/x0\n",
    "    alpha_t=alpha*exp(-omega_x*t*1im)\n",
    "    return ( 1.0./sqrt(x0*sqrt(pi))*exp(-0.5im*omega_x*t)\n",
    "           *exp(sqrt(2.0)*alpha_t*xi - 0.5*xi.^2 - real(alpha_t)*alpha_t) )\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t0 = 0\n",
    "tend = 1\n",
    "psi = wave_function(method)\n",
    "psi_ref = wave_function(method)\n",
    "set!(psi, coherent_state, t0)        # initial data at t=t0\n",
    "set!(psi_ref, coherent_state, tend)  # reference solution at t=tend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f259481ef50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(get_nodes(method), abs(get_data(psi)).^2)\n",
    "hold(true)\n",
    "plot(get_nodes(method), abs(get_data(psi_ref)).^2)\n",
    "hold(false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             dt         err      p\n",
      "-----------------------------------\n",
      "  1   1.000e+00   3.260e-01\n",
      "  2   5.000e-01   7.018e-02   2.22\n",
      "  3   2.500e-01   1.691e-02   2.05\n",
      "  4   1.250e-01   4.191e-03   2.01\n",
      "  5   6.250e-02   1.045e-03   2.00\n",
      "  6   3.125e-02   2.612e-04   2.00\n",
      "  7   1.563e-02   6.528e-05   2.00\n",
      "  8   7.813e-03   1.632e-05   2.00\n",
      "  9   3.906e-03   4.080e-06   2.00\n",
      " 10   1.953e-03   1.020e-06   2.00\n",
      " 11   9.766e-04   2.550e-07   2.00\n",
      " 12"
     ]
    }
   ],
   "source": [
    "global_orders(psi, psi_ref, t0, tend, tend-t0, scheme=Strang, rows=12) \n",
    "; "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   4.883e-04   6.375e-08   2.00\n"
     ]
    }
   ],
   "source": [
    "include(\"time_stepper.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             dt         err      p         err      p\n",
      "------------------------------------------------------\n",
      "  1   1.000e+00   3.260e-01          1.012e-01\n",
      "  2   5.000e-01   4.803e-02   2.76   3.798e-03   4.74\n",
      "  3   2.500e-01   6.205e-03   2.95   2.847e-04   3.74\n",
      "  4   1.250e-01   7.818e-04   2.99   1.903e-05   3.90\n",
      "  5   6.250e-02   9.792e-05   3.00   1.210e-06   3.97\n",
      "  6   3.125e-02   1.225e-05   3.00   7.597e-08   3.99\n",
      "  7   1.563e-02   1.531e-06   3.00   4.753e-09   4.00\n",
      "  8   7.813e-03   1.914e-07   3.00   2.972e-10   4.00\n",
      "  9   3.906e-03   2.392e-08   3.00   1.857e-11   4.00\n",
      " 10   1.953e-03   2.990e-09   3.00   1.161e-12   4.00\n"
     ]
    }
   ],
   "source": [
    "local_orders(psi, coherent_state, t0, tend-t0, DefectBasedScheme(Strang, 2), operator_sequence=\"AB\", rows=10)\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             dt         err      p\n",
      "-----------------------------------\n",
      "  1   1.000e+00   5.280e-04\n",
      "  2   5.000e-01   1.032e-05   5.68\n",
      "  3   2.500e-01   4.391e-07   4.55\n",
      "  4   1.250e-01   1.607e-08   4.77\n",
      "  5   6.250e-02   5.405e-10   4.89\n",
      "  6   3.125e-02   1.750e-11   4.95\n",
      "  7   1.563e-02   5.568e-13   4.97\n"
     ]
    }
   ],
   "source": [
    "scheme_5 = ( 0.201651044312324230,   0.578800656272664932, \n",
    "             0.562615975356569200,   0.273128836056524479, \n",
    "             0.253874038247554845,  -0.102733803148432142, \n",
    "            -0.835351693190370636,   0.068014946093165092, \n",
    "             0.068014946093165092,  -0.835351693190370636,\n",
    "            -0.102733803148432142,   0.253874038247554845, \n",
    "             0.273128836056524479,   0.562615975356569200, \n",
    "             0.578800656272664932,   0.201651044312324230 )          \n",
    "global_orders(psi, psi_ref, t0, tend, tend-t0, scheme=scheme_5, rows=7) \n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             dt         err      p         err      p\n",
      "------------------------------------------------------\n",
      "  1   1.000e+00   5.280e-04          2.275e-04\n",
      "  2   5.000e-01   7.664e-06   6.11   8.091e-07   8.14\n",
      "  3   2.500e-01   1.354e-07   5.82   4.341e-09   7.54\n",
      "  4   1.250e-01   2.185e-09   5.95   3.040e-11   7.16\n",
      "  5   6.250e-02   3.441e-11   5.99   2.358e-13   7.01\n",
      "  6   3.125e-02   5.388e-13   6.00   2.403e-14   3.29\n"
     ]
    }
   ],
   "source": [
    "local_orders(psi, coherent_state, t0, tend-t0, DefectBasedScheme(scheme_5, 5), operator_sequence=\"AB\", rows=6)\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             dt         err      p         err      p\n",
      "------------------------------------------------------\n",
      "  1   1.000e+00   5.280e-04          8.989e-04\n",
      "  2   5.000e-01   7.664e-06   6.11   6.347e-06   7.15\n",
      "  3   2.500e-01   1.354e-07   5.82   4.825e-08   7.04\n",
      "  4   1.250e-01   2.185e-09   5.95   3.743e-10   7.01\n",
      "  5   6.250e-02   3.441e-11   5.99   2.919e-12   7.00\n",
      "  6   3.125e-02   5.388e-13   6.00   2.276e-14   7.00\n"
     ]
    }
   ],
   "source": [
    "local_orders(psi, coherent_state, t0, tend-t0, PalindromicScheme(scheme_5, 5), operator_sequence=\"AB\", rows=6)\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TSSM.SchroedingerHermite1D{Float64}(Ptr{Void} @0x00000000070d83e0)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx = 2048\n",
    "method = SchroedingerHermite1D(nx, omega_x, hbar=hbar, mass=mass, potential=harmonic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.445106651960332e-16"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0 = 0\n",
    "tend = 1\n",
    "psi = wave_function(method)\n",
    "psi_ref = wave_function(method)\n",
    "set!(psi, coherent_state, t0)        # initial data at t=t0\n",
    "set!(psi_ref, coherent_state, tend)  # reference solution at t=tend\n",
    "\n",
    "propagate_A!(psi, tend-t0)\n",
    "distance(psi, psi_ref)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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